Current Interruption Transients Calculation

David F. Peelo, Consultant, former Specialist Engineer at BC Hydro, Vancouver, Canada David Peelo joined BC Hydro in Vancouver in 1973, first in the Quality Assurance Department, then from 1981 in the Stations Engineering Division as a switchgear and switching specialist. He left BC Hydro in 2001 to become an independent consultant with clients in Australia, Canada, US, India and Korea, teaching advanced courses on surge arrester application, switchgear application and switching in high voltage networks. He has had active leading roles in standards development in IEEE and the International Electrotechnical Commission (IEC). David has authored over 60 technical papers and lead the development of an IEEE guide and IEC standard for shunt reactor switching. He is recipient of the CIGRE Distinguished Member Award and the IEC 1906 Award, and a Fellow of the Institution of Electrical Engineers.

Preface ix 1 Introduction 1 1.1 Background 1 1.2 Short-Circuit Rating Basis for High-Voltage Circuit Breakers 2 1.3 Current Interruption Terminology 4 Bibliography 7 2 RLC Circuits 8 2.1 General 8 2.2 Series RLC Circuit with Step Voltage Injection 8 2.3 Source-Free Series RLC Circuit with Precharged Capacitor 15 2.4 Source-Free Parallel RLC Circuit with Precharged Capacitor 18 2.5 Parallel RLC Circuit with Ramp Current Injection 21 2.6 Alternative Equations 27 2.7 Travelling Wave Basics 28 2.8 Summary 32 Bibliography 32 3 Pole Factor Calculation 33 3.1 General 33 3.2 Pole Factors: Effectively Earthed Systems 43 3.3 Pole Factors: Non-Effectively Earthed Systems 51 3.4 Alternative Pole Factor Calculation Method 56 3.5 Three-Phase Test Circuit Arrangement 57 3.6 Summary 59 Bibliography 60 4 Terminal Faults 61 4.1 General Considerations 61 4.2 Standard TRV Derivation 63 4.3 Effect of Added Capacitance 72 4.4 Effect of Added Resistance 83 4.5 Effect of Added Inductance 84 4.6 Out-of-Phase Switching 90 4.7 Asymmetrical Currents 91 4.8 Double Earth Faults 99 4.9 Summary 102 Bibliography 103 5 Short-Line Faults 104 5.1 General 104 5.2 Line-Side Voltage Calculation 104 5.3 Effect of Added Capacitance 115 5.4 Discussion 118 Bibliography 119 6 Inductive Load Switching 120 6.1 General 120 6.2 General Shunt Reactor Switching Case 123 6.3 Shunt Reactors with Isolated Neutrals 130 6.4 Shunt Reactors with Neutral Reactor Earthed Neutrals 135 6.5 Shunt Reactors with Earthed Neutrals 136 6.6 Re-Ignitions 137 6.7 Unloaded Transformer Switching 139 6.8 Discussion 139 6.9 Summary 139 Bibliography 140 7 Capacitive Load Switching 141 7.1 General 141 7.2 Shunt Capacitor Banks 141 7.2.1 Energization 141 7.2.2 De-Energization 152 7.2.3 Outrush 159 7.3 Transmission Lines 160 7.4 Cables 163 7.5 Summary 165 Bibliography 166 8 Circuit Breaker Type Testing 167 8.1 Introduction 167 8.2 Circuit Breaker Interrupting Time 167 8.3 Inherent Transient Recovery Voltages 173 8.4 Inductive Load Switching 174 8.5 Capacitive Current Switching 175 Bibliography 175 Appendix A: Differential Equations 177 Bibliography 186 Appendix B: Principle of Duality 187 Appendix C: Useful Formulae 190 Appendix D: Euler s Formula 193 Bibliography 196 Appendix E: Asymmetrical Current-Calculating Areas Under Curves 197 Appendix F: Shunt Reactor Switching: First-Pole-to-Clear Circuit Representation 200 Appendix G: Special Case: Interrupting Small Capacitive Currents 207 Bibliography 210 Appendix H: Evolution of Transient Recovery Voltages 211 H.1 Introduction 211 H.2 TRVs: Terminal Faults 212 H.3 Terminal Fault TRV Standardization 218 H.4 Short-Line Fault 220 H.5 Inductive and Capacitive Load Current Switching 221 H.6 Terminal Fault TRV Calculation 221 H.6.1 Pole Factor Calculation 221 H.6.2 Transient Calculation 225 Bibliography 226 Index 231